用符号回归提升流体模拟精度，兼具可解释性与泛化能力
Symbolic Regression of Data-Driven Reduced Order Model Closures for Under-Resolved, Convection-Dominated Flows
- 采用符号回归构建新型数据驱动闭合项，融合结构模型与神经网络优势
- 在雷诺数10000至20000下，对绕圆柱流和腔体流测试均表现更优
- 结果可解释、参数少、鲁棒性强，适合高保真流体仿真研究者
数据驱动闭合项可提升欠解析、对流主导流场中标准降阶模型（ROM）的精度。现有方法分为两类：(i) 结构型，采用简单假设（如线性或二次）；(ii) 基于机器学习，使用神经网络假设。本文提出一种新型符号回归（SR）数据驱动闭合策略，结合二者优势并消除其缺陷。所提新闭合项使降阶模型具备可解释性、简洁性、高精度、强泛化性和鲁棒性。为验证效果，采用数据驱动变分多尺度降阶模型框架，在绕圆柱流和雷诺数为10000、15000、20000的盖式腔流两个典型问题上进行数值对比。结果表明，新符号回归闭合项生成的降阶模型在准确性和鲁棒性上均优于传统结构型与机器学习型闭合方案。
原文摘要 · Abstract (English)
Data-driven closures correct the standard reduced order models (ROMs) to increase their accuracy in under-resolved, convection-dominated flows. There are two types of data-driven ROM closures in current use: (i) structural, with simple ansatzes (e.g., linear or quadratic); and (ii) machine learning-based, with neural network ansatzes. We propose a novel symbolic regression (SR) data-driven ROM closure strategy, which combines the advantages of current approaches and eliminates their drawbacks. As a result, the new data-driven SR closures yield ROMs that are interpretable, parsimonious, accurate, generalizable, and robust. To compare the data-driven SR-ROM closures with the structural and machine learning-based ROM closures, we consider the data-driven variational multiscale ROM framework and two under-resolved, convection-dominated test problems: the flow past a cylinder and the lid-driven cavity flow at Reynolds numbers Re = 10000, 15000, and 20000. This numerical investigation shows that the new data-driven SR-ROM closures yield more accurate and robust ROMs than the structural and machine learning ROM closures.
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